We here report on multiwavelength ( X–ray to optical ) followup observations of carbon star CGCS 5926 . These were motivated by the fact that this star is positionally coincident with a faint X–ray emitting object belonging to the ROSAT catalog of sources , thus suggesting a possible symbiotic X–ray binary ( SyXB ) nature for it . Our spectrophotometric optical data confirm the giant carbon star nature of the object and allow us to classify its spectral type as C ( 6,2 ) . This classification places CGCS 5926 at a distance of \sim 5 kpc from Earth . BVR _ { C } I _ { C } photometry of the star shows that it displays a variability of \sim 0.3 mag on timescales of months , with the star getting bluer when its brightness increases . Our photometric data indicate a periodicity of 151 days , which we explain as due to radial pulsations of CGCS 5926 on the basis of its global characteristics . The source is not detected at X–rays with Swift /XRT down to a 0.3–10 keV band luminosity of \approx 3 \times 10 ^ { 32 } erg s ^ { -1 } . This nondetection is apparently in contrast with the ROSAT data ; however we show that , even if the probability that CGCS 5926 can be a SyXB appears quite low , the present information does not completely rule out such a possibility , while it makes other interpretations even more unlikely if we assume that the ROSAT detection was real . This issue might thus be settled by future , more sensitive , observations at high energies .